Control variable methods in the simulation of a model of a multiprogrammed computer system

One approach to the evaluation of the performance of multiprogranmed computer systems includes the development of Monte Carlo simulations of transitions of programs within such systems, and their strengthening by control variable and concomitant variable methods. An application of such a combination of analytical, numerical, and Monte Carlo approaches to a model of system overhead in a paging machine is presented.     

On estimation in weibull distributions with random scale parameters

Work by the present authors on life distributions derived from stochastic hazard functions [4] is related to certain articles that have appeared in this journal. This relationship is illustrated. The emphasis of this article is upon problems of parameter estimation.     

A new derivation of the logistic distribution

Logistic distribution is widely used in describing biological, engineering, industrial, and various other types of data. In this paper it is shown that this distribution is a special case of a compound generalized extreme value distribution which is derived by compounding a generalized extreme value distribution with a gamma distribution. The paper contains several useful results relevant to these distribution functions.     

War reserve spares kits supplemented by normal operating assets

In peacetime, base stock levels of spares are determined on the assumption of normal resupply from the depot. In the event of war, however, a unit must be prepared to operate from stock on hand for a period of time without being resupplied from the depot. This paper describes a mathematical model for determining such war reserve spares (WRS) requirements. Specifically, the model solves the following kind of optimization problem: find the least-cost WRS kits that will keep the probability of a stockout after K cannibalizations less than or equal to some target objective α. The user of the model specifies the number of allowable cannibalizations, and the level of protection that the kit is supposed to provide. One interesting feature of this model is that in the probability computation it takes into account the possiblility of utilizing normal base operating assets. Results of a sensitivity analysis indicate that if peacetime levels were explicitly taken into account when designing a WRS kit, a cost saving of nearly 40 percent could be effected without degrading base supply performance in wartime.     

A maximum utility solution to a vehicle constrained tanker scheduling problem

A modification to the Dantzig and Fulkerson Tanker Scheduling Problem is described. An insufficient number of vehicles and a utility associated with each vehicle delivery are assumed. The new problem is shown to be equivalent to a Transshipment Problem, the solution of which is the same as the maximal utility solution of the modified Tanker Scheduling Problem. An example is given.     

The effect of correlated exponential service times on single server tandem queues

An investigation via simulation of system performance of two stage queues in series (single server, first-come, first-served) under the assumption of correlated exponential service times indicates that the system's behavior is quite sensitive to departures from the traditional assumption of mutually independent service times, especially at higher utilizations. That service times at the various stages of a tandem queueing system for a given customer should be correlated is intuitively appealing and apparently not at all atypical. Since tandem queues occur frequently, e.g. production lines and the logistics therewith associated, it is incumbent on both the practitioner and the theoretician that they be aware of the marked effects that may be induced by correlated service times. For the case of infinite interstage storage, system performance is improved by positive correlation and impaired by negative correlation. This change in system performance is reversed however for zero interstage storage and depends on the value of the utilization rate for the case where interstage storage equals unity. The effect due to correlation is shown to be statistically significant using spectral analytic techniques. For correlation equal unity and infinite interstage storage, results are provided for two through twenty-five stages in series to suggest how adding stages affects system performance for ρ>0. In this extreme case of correlation, adding stages has an effect on system performance which depends markedly on the utilization rate. Recursive formulae for the waiting time per customer for the cases of zero, one, and infinite interstage storage are derived.     

Probabilistic priorities in the M/G/1 queue

A simple method is presented for deriving the mean and variance of the queueing time distribution in an M/G/1 queue when the priorities assigned to customers have an assignment probability distribution. Several examples illustrate the results. The mean and variance of the queueing time distribution for the longest service time discipline are derived, and its disadvantages are discussed.     

A primal simplex algorithm to solve a rectilinear distance facility location problem

This paper considers the problem of locating m new facilities in the plane so as to minimize a weighted rectangular distance between the new facilities and n existing facilities. A special purpose primal simplex algorithm is developed to solve this problem. The algorithm will maintain at all times a basis of dimension m by m; however, because of the triangularity of the basis matrix, it will not be necessary to form a basis inverse explicitly.     

Storage problems when demand is “all or nothing”

An inventory of physical goods or storage space (in a communications system buffer, for instance) often experiences “all or nothing” demand: if a demand of random size D can be immediately and entirely filled from stock it is satisfied, but otherwise it vanishes. Probabilistic properties of the resulting inventory level are discussed analytically, both for the single buffer and for multiple buffer problems. Numerical results are presented.